Finite mixtures of regressions with fixed covariates are a commonly used model-based clustering methodology to deal with regression data. However, they assume assignment independence, i.e., the allocation of data points to the clusters is made independently of the distribution of the covariates. To take into account the latter aspect, finite mixtures of regressions with random covariates, also known as cluster-weighted models (CWMs), have been proposed in the univariate and multivariate literature. In this paper, the CWM is extended to matrix data, e.g., those data where a set of variables are simultaneously observed at different time points or locations. Specifically, the cluster-specific marginal distribution of the covariates and the cluster-specific conditional distribution of the responses given the covariates are assumed to be matrix normal. Maximum likelihood parameter estimates are derived using an expectation-conditional maximization algorithm. Parameter recovery, classification assessment, and the capability of the Bayesian information criterion to detect the underlying groups are investigated using simulated data. Finally, two real data applications concerning educational indicators and the Italian non-life insurance market are presented.

具有固定协变量的回归的有限混合是一种常用的基于模型的聚类方法来处理回归数据。然而，他们假设分配独立，即数据点到集群的分配独立于协变量的分布。考虑到后一方面，单变量和多变量文献中已经提出了具有随机协变量的回归的有限混合，也称为聚类加权模型 (CWM)。在本文中，CWM 被扩展到矩阵数据，例如，在不同时间点或位置同时观察到一组变量的那些数据。具体而言，协变量的特定于集群的边际分布和给定协变量的响应的特定于集群的条件分布被假定为矩阵正态分布。使用期望条件最大化算法导出最大似然参数估计。使用模拟数据研究参数恢复、分类评估和贝叶斯信息标准检测基础组的能力。最后，介绍了关于教育指标和意大利非寿险市场的两个真实数据应用。